The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

Author： Gutik O.   Pagon D.   Repovš D.  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.124, Iss.3, 2009-08, pp. : 201-214

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Abstract

We search for conditions on a countably compact (pseudocompact) topological semigroup under which: (i) each maximal subgroup H(e) in S is a (closed) topological subgroup in S; (ii) the Clifford part H(S) (i.e. the union of all maximal subgroups) of the semigroup S is a closed subset in S; (iii) the inversion inv: H(S) → H(S) is continuous; and (iv) the projection π: H(S) → E(S), π: x ↦ xx −1, onto the subset of idempotents E(S) of S, is continuous.

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